Hydrodynamical acceleration of particles in supernovae and extragalactic radio sources

The acceleration of cosmic particles to relativistic energies as the result of the propagation of relativistic, hydrodynamical shocks is reviewed. The supernova-shock model of Colgate and Johnson for acceleration of cosmic-ray nuclei is described and assessed, with emphasis on the underlying hydrodynamics. We review the evidence for relativistic blast waves in compact radio sources and describe the models which have been calculated. We point out that these models lead naturally to a consideration of non-spherical relativistic blast waves which are both accelerated and focused by the ambient gas distribution. We then describe recent work which extends the spherically symmetric, ultra-relativistic solutions which have been found to cases involving arbitrarily relativistic shocks in an axisymmetric density profile. Lastly, we discuss the development of an Eulerian numerical scheme for special-relativistic hydrodynamics